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Simultaneous equations

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by vinay1983 » Wed Sep 11, 2013 4:27 am
lf the average (arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers?

(1) The range of the n integers is 14.

(2) The greatest of the n integers is 17

Source: OG Q-2 ED OA D

I did this

Acc to me consecutive odd integers x+1, x+3, x+5..so on

Statement 1

Range = 14, so greatest integer value-smallest integer value=14. This can be any numbers...So Insuff

Statement 2

Greatest integer value is 17. By this alone we cannot tell anything about the least integer

Combining 1 & 2

17-14=3

So 3, 5, 7, 9, 11, 13, 15, 17 Sufficient. Where am I wrong?
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Wed Sep 11, 2013 5:42 am
vinay1983 wrote:If the average (arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers?

(1) The range of the n integers is 14.

(2) The greatest of the n integers is 17

Source: OG Q-2 ED OA D

I did this

Acc to me consecutive odd integers x+1, x+3, x+5..so on

Statement 1

Range = 14, so greatest integer value-smallest integer value=14. This can be any numbers...So Insuff

Statement 2

Greatest integer value is 17. By this alone we cannot tell anything about the least integer

Combining 1 & 2

17-14=3

So 3, 5, 7, 9, 11, 13, 15, 17 Sufficient. Where am I wrong?
You are not using the given information that the average (arithmetic mean) of n consecutive odd integers is 10.

Cheers,
Brent
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by Brent@GMATPrepNow » Wed Sep 11, 2013 6:01 am
vinay1983 wrote:lf the average (arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers?

(1) The range of the n integers is 14.

(2) The greatest of the n integers is 17
Target question: What is the least of the integers?

Statement 1: The range of the n integers is 14.
There's a nice rule that says, "In a set where the numbers are equally spaced, the mean will equal the median."
Since consecutive odd integers are equally spaced, the mean of the integers will equal the median.
So, we know that the "middlemost" value is 10.
Since 10 is not odd, we now know that there must be an even number of odd integers in the set, and the average of the TWO MIDDLEMOST integers is 10.
If the median is 10, then half of the odd integer are greater than 10, and half are less than 10.
Since the range is 14, we know that the greatest value is 10+7 and the least value is 10-7
So, the integers are 3,5,7,9,11,13,15,17, which means the smallest value is 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The greatest of the n integers is 17
There's another nice rule that says, In a set where the numbers are equally spaced, the mean = (largest value - smallest value)/2
So, we know that 10 = (17 - smallest value)/2
From this, we can conclude that the smallest value must be 3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent
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by Java_85 » Wed Sep 11, 2013 9:15 am
IMO D , both statements are separately sufficient.
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by [email protected] » Thu Sep 12, 2013 1:41 pm
Hi vinay1983,

This DS question hides an interesting Number Property that you'll find useful.

If you're dealing with consecutive odd integers with an average of 10, then the possibilities will follow a pattern...

The numbers COULD be:

9, 11
7, 9, 11, 13
5, 7, 9, 11, 13, 15
3, 5, 7, 9, 11, 13, 15, 17
etc

The pattern is that there will be an EQUAL number of terms above 10 and below 10. You can use THAT pattern along with the other info to CRUSH this question relatively quickly.

Fact 1: The range is 14.

Look at the examples above. There's only one group with a range of 14. The other groups would either have a smaller range or a larger range.
Fact 1 is SUFFICIENT.

Fact 2: The greatest value is 17

Again, look at the examples above. There's only one group with 17 as the largest number.
Fact 2 is SUFFICIENT.

Final AsnwerD

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